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Find the values of m and n if : 4^(2m)...

Find the values of m and n if :
`4^(2m)=(root(3)(16))^(-(6)/(n))=(sqrt(8))^(2)`

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The correct Answer is:
`m = (3)/(4) and n = - (8)/(3)`
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ICSE-INDICES [EXPONENTS]-EXERCISE 7 (B)
  1. Solve : 3^(x2) : 3^(x) = 9 : 1

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  2. Solve : 8 xx 2^(2x) + 4 xx 2^(x +1) = 1 + 2^(x)

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  3. Solve : 2^(2x) + 2^(x+2) - 4 xx 2^(3) = 0

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  4. Solve : (sqrt(3))^(x-3)=(sqrt(3))^((x+1)/4)

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  5. Find the values of m and n if : 4^(2m)=(root(3)(16))^(-(6)/(n))=(sqr...

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  6. Solve for x and y if : (sqrt(32))^(x)÷2^(y+1)= 1 and 8^(y)-16^(4-(x)...

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  7. If x is a positive real number and the exponents are rational numbe...

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  8. Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1 ((x^(a+b))^2...

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  9. If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

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  10. If a^x=b^y=c^2a n d\ b^2=a c , prove that y=(2x z)/(x+z)

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  11. If 5^(-p)=4^(-q)=20^(r ). Show that (1)/(p)+(1)/(q)+(1)/(r )=0

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  12. If m =! n and (m + n)^(-1) (m^(-1) + n^(-1)) = m^(x) n^(y), show that ...

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  13. If 5^(x +1) = 25^(x-2), find the value of 3^(x-3) xx 2^(3-x).

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  14. If 4^(x+3)=112+8xx4^(x), find (18x)^(3x)

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  15. Solve for x : 4^(x-1)xx(0.5)^(3-2x)=((1)/(8))^(-x)

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  16. Solve for x : (a^(3x+5))^(2) . (a^(x))^(4) = a^(8x+12).

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  17. Solve for x : (81)^((3)/(4))-((1)/(32))^(-(2)/(5))+x((1)/(2))^(-1).2^(...

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  18. Solve for x : 2^((3x + 3)) = 2^((3x + 1)) + 48.

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  19. Solve for x : 3(2^(x) + 1) - 2^(x + 2)) + 5 = 0.

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  20. Solve for x : 9^(x + 2)) = 720 + 9^(x)

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